A Generalized Algebraic Method for Constructing a Series of Explicit Exact Solutions of a (1+1)-Dimensional Dispersive Long Wave Equation**The project supported by the National Outstanding Youth Foundation of China under Grant No. 19925522 and National Natural Science Foundation of China under Grant No. 90203001

Abstract

Making use of a new and more general ansatz, we present the generalized algebraic method to uniformly construct a series of new and general travelling wave solution for nonlinear partial differential equations. As an application of the method, we choose a (1+1)-dimensional dispersive long wave equation to illustrate the method. As a result, we can successfully obtain the solutions found by the method proposed by Fan [E. Fan, Comput. Phys. Commun. 153 (2003) 17] and find other new and more general solutions at the same time, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solutions, hyperbolic and soliton solutions, Jacobi and Weierstrass doubly periodic wave solutions.